There 70 women in a club. 20 play volley ball only ,10 play basketball only , 6 play tennis ball only. 4 play all the games and an equal number play two games only. Illustrate this information in a Venn diagram. Find the number of women who play volleyball.
More explanation please
To illustrate this information in a Venn diagram, we can start by drawing three overlapping circles to represent volleyball (V), basketball (B), and tennis (T). We'll label the regions where the circles overlap with combinations of the game names.
Next, we can fill in the known values. We know that there are 70 women in total, and we're given that 20 play volleyball only (V), 10 play basketball only (B), and 6 play tennis only (T). Additionally, 4 women play all three games (V, B, T).
To find the number of women who play volleyball, we need to determine the number of women who play volleyball only (V), as well as those who play volleyball and another game. We're told that an equal number of women play two games only, so let's call this number "x".
Based on these relationships, we can start filling in the diagram:
```
_______
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/__________\__________\
| V | B | T |
| | | |
|_____ |_____|_____|
(20) (x) (6)
```
Now, let's determine the number of women who play two games only. Since we're told that an equal number play two games only, we can assign "x" to both regions where circles overlap:
```
_______
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/__________\__________\
| V | B | T |
| | | |
|_____ |_____|_____|
(20) (x) (6)
```
Finally, we can calculate the value of "x". We know that there are a total of 70 women in the club, so the sum of all the regions in the Venn diagram should add up to 70. Based on the diagram, we have:
V + B + T + x + x + 20 + 10 + 6 = 70
Simplifying the equation:
2x + V + B + T + 20 + 10 + 6 = 70
2x + V + B + T + 36 = 70
2x + V + B + T = 70 - 36
2x + V + B + T = 34
Since we know that 4 women play all three games (V, B, T), we can substitute V + B + T with 4:
2x + 4 = 34
2x = 34 - 4
2x = 30
x = 30 / 2
x = 15
Now, we can fill in the diagram with the calculated values:
```
_______
/ \
/ \
/ 4 \
/ \
/ \
/ \
/ \
/ \
/__________\__________\
| V | B | T |
| | | |
|____15_|______|__15__|
(20) (15) (6)
```
From the diagram, we can see that there are 20 women who play volleyball only (V). Therefore, the number of women who play volleyball is 20.
more explanation
Did you follow the instructions and draw the Venn diagram ? (we can't do that in this format)
I labeled my circles V, B, and T and placed 4 in the intersection of all three and 20, 10, and 6 in the appropriate places of the circles. I placed an x in the volleyball-tennis "only" intersection, an x in the basket-ball only intersection in an x in the volleyball-basketball only intersection.
then, x + x + x + 4 + 20 + 10 + 6 = 70
3x = 30
x = 10
take it from there